Steam Train: Boiler Pressure & Tractive Effort (2D)

This 2D companion strips the 3D locomotive scene down to the mechanics that actually decide how a steam engine pulls a train. Boiler pressure, cylinder bore, piston stroke and driving-wheel diameter feed directly into the real locomotive-engineering tractive-effort formula, TE = 0.85·P·d²·s/D, so every slider measurably changes the starting pull at the rail. Boiler saturation temperature is derived from a real water Antoine-equation pressure-temperature relation rather than a fixed number, and a live tractive-effort-versus-speed chart shows the classic locomotive performance curve: effort holds flat at its starting value while the valve gear can still admit steam for a full stroke, then falls off as speed rises past a corner speed where the boiler can no longer refill the cylinders fast enough — the same constant-effort-then-constant-power shape real steam locomotives trace. Net accelerating force is tractive effort minus rolling resistance and grade force, integrated against the trailing load's mass, so a heavier train or a steeper grade genuinely cuts both acceleration and top speed.